   Chapter 16, Problem 5RE

Chapter
Section
Textbook Problem

Evaluate the line integral.5. ∫C y3 dx + x2 dy, C is the arc of the parabola x = 1 − y2 from (0, −1) to (0, 1)

To determine

To Evaluate: The line integral Cy3dx+x2dy , C is the arc of the parabola x=1y2 from (0,1) to (0,1) .

Explanation

Given data:

The parametric equation of curve and its limits are given as follows.

x=1y2 from (0,1) to (0,1) .

Formula used:

Write the expression to evaluate the line integral for a function f(x,y) along the curve C .

CP(x,y)dx+Q(x,y)dy=CP(x,y)dx+CQ(x,y)dy

CP(x,y)dx+Q(x,y)dy=[abP(x(t),y(t))x(t)dt+abQ(x(t),y(t))y(t)dt] (1)

Write the required differential and integration formulae to evaluate the given integral.

ddxxn=nxn1[f(x)]ndx=[f(x)]n+1n+1

Consider the expression x=1y2 .

x=1y2

Differentiate the equation with respect to y .

dxdy=02ydx=(2y)dy

Modify equation (1) as follows

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